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K-means Principal Geodesic Analysis on Riemannian Manifolds

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Proceedings of the Future Technologies Conference (FTC) 2019 (FTC 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1069))

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Abstract

Principal geodesic analysis (PGA) has been proposed for data dimensionality reduction on manifolds. However, a single PGA model is limited to data with a single modality. In this paper, we are the first to propose a generalized K-means-PGA model on manifolds. This model can analyze multi-mode nonlinear data, which applies to more manifolds (Sphere, Kendall’s shape and Grassmannian). To show the applicability of our model, we apply our model to spherical, Kendall’s shape and Grassmannian manifolds. Our K-means-PGA model offers correct geometry geodesic recovery than K-means-PCA model. We also show shape variations from different clusters of human corpus callosum and mandible data. To demonstrate the efficiency of our model, we perform face recognition using ORL dataset. Our model has a higher accuracy (99.5%) than K-means-PCA model (95%) in Euclidean space.

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Notes

  1. 1.

    Source code is available at: https://github.com/heaventian93/Kmeans-Principal-Geodesic-Analysis.

  2. 2.

    https://sites.google.com/site/hpardoe/cc_abide.

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Author information

Authors and Affiliations

  1. Computer Science and Engineering, Lehigh University, Bethlehem, PA, 18015, USA

    Youshan Zhang

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  1. Youshan Zhang
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Correspondence to Youshan Zhang .

Editor information

Editors and Affiliations

  1. Faculty of Science and Engineering, Saga University, Saga, Japan

    Kohei Arai

  2. The Science and Information (SAI) Organization, Bradford, West Yorkshire, UK

    Rahul Bhatia

  3. The Science and Information (SAI) Organization, Bradford, West Yorkshire, UK

    Supriya Kapoor

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Zhang, Y. (2020). K-means Principal Geodesic Analysis on Riemannian Manifolds. In: Arai, K., Bhatia, R., Kapoor, S. (eds) Proceedings of the Future Technologies Conference (FTC) 2019. FTC 2019. Advances in Intelligent Systems and Computing, vol 1069. Springer, Cham. https://doi.org/10.1007/978-3-030-32520-6_42

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